Optimal. Leaf size=43 \[ -\frac {a^3}{21 x^{21}}-\frac {a^2 b}{6 x^{18}}-\frac {a b^2}{5 x^{15}}-\frac {b^3}{12 x^{12}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {272, 45}
\begin {gather*} -\frac {a^3}{21 x^{21}}-\frac {a^2 b}{6 x^{18}}-\frac {a b^2}{5 x^{15}}-\frac {b^3}{12 x^{12}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 45
Rule 272
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^3}{x^{22}} \, dx &=\frac {1}{3} \text {Subst}\left (\int \frac {(a+b x)^3}{x^8} \, dx,x,x^3\right )\\ &=\frac {1}{3} \text {Subst}\left (\int \left (\frac {a^3}{x^8}+\frac {3 a^2 b}{x^7}+\frac {3 a b^2}{x^6}+\frac {b^3}{x^5}\right ) \, dx,x,x^3\right )\\ &=-\frac {a^3}{21 x^{21}}-\frac {a^2 b}{6 x^{18}}-\frac {a b^2}{5 x^{15}}-\frac {b^3}{12 x^{12}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 43, normalized size = 1.00 \begin {gather*} -\frac {a^3}{21 x^{21}}-\frac {a^2 b}{6 x^{18}}-\frac {a b^2}{5 x^{15}}-\frac {b^3}{12 x^{12}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.12, size = 36, normalized size = 0.84
method | result | size |
default | \(-\frac {a^{3}}{21 x^{21}}-\frac {a^{2} b}{6 x^{18}}-\frac {a \,b^{2}}{5 x^{15}}-\frac {b^{3}}{12 x^{12}}\) | \(36\) |
norman | \(\frac {-\frac {1}{21} a^{3}-\frac {1}{6} a^{2} b \,x^{3}-\frac {1}{5} a \,b^{2} x^{6}-\frac {1}{12} b^{3} x^{9}}{x^{21}}\) | \(37\) |
risch | \(\frac {-\frac {1}{21} a^{3}-\frac {1}{6} a^{2} b \,x^{3}-\frac {1}{5} a \,b^{2} x^{6}-\frac {1}{12} b^{3} x^{9}}{x^{21}}\) | \(37\) |
gosper | \(-\frac {35 b^{3} x^{9}+84 a \,b^{2} x^{6}+70 a^{2} b \,x^{3}+20 a^{3}}{420 x^{21}}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.30, size = 37, normalized size = 0.86 \begin {gather*} -\frac {35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.33, size = 37, normalized size = 0.86 \begin {gather*} -\frac {35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.18, size = 39, normalized size = 0.91 \begin {gather*} \frac {- 20 a^{3} - 70 a^{2} b x^{3} - 84 a b^{2} x^{6} - 35 b^{3} x^{9}}{420 x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.48, size = 37, normalized size = 0.86 \begin {gather*} -\frac {35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 37, normalized size = 0.86 \begin {gather*} -\frac {\frac {a^3}{21}+\frac {a^2\,b\,x^3}{6}+\frac {a\,b^2\,x^6}{5}+\frac {b^3\,x^9}{12}}{x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________